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GEOMETRICP

Updated 2024-03-08 16:17:19.437000

Syntax

SELECT [westclintech].[wct].[GEOMETRICP] (
  <@X, float,>
 ,<@P, float,>)

Description

Use the scalar function GEOMETRICP to calculate the cumulative distribution function of the geometric distribution.

The formula for the cumulative distribution function is:

Pr(k;p)=1-(1-p)^{{\lfloor{k}\rfloor}+1}

Arguments

@P

is the probability of success. @P is an expression of type float or of a type that implicitly converts to float.

@X

is the number of failures. @X is an expression of type float or of a type that implicitly converts to float.

Return Type

float

Remarks

@X must be greater than or equal to zero (@X ≥ 0).

@P must be greater than zero and less than or equal to one (0 < @P ≤ 1).

For the probability mass function, use GEOMETRIC.

For the upper cumulative distribution use 1 – GEOMTRICP(@X-1, @P).

Examples

Calculate the cumulative distribution function:

SELECT wct.GEOMETRICP(3, 0.4);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.8704"}]}

You can use the SeriesInt function from the XLeratorDB/math library to generate a dataset which can be pasted into EXCEL to generate a graph of the cumulative distribution function.

SELECT SeriesValue,

       wct.GEOMETRICP(SeriesValue, 0.1) as [f(x,0.1)],

       wct.GEOMETRICP(SeriesValue, 0.3) as [f(x,0.3)],

       wct.GEOMETRICP(SeriesValue, 0.5) as [f(x,0.5)],

       wct.GEOMETRICP(SeriesValue, 0.7) as [f(x,0.7)],

       wct.GEOMETRICP(SeriesValue, 0.9) as [f(x,0.9)]

FROM wct.SeriesInt(0, 10, NULL, NULL, NULL);

This is an EXCEL-generated graph of the results.

http://westclintech.com/Portals/0/images/doc_stats_GEOMETRICP_img1.jpg